Can ‘Cause’ Explain Wavefunction Collapse? My Proposal for a Dynamical Model

I’ve been working on a conceptual framework that connects classical causality with quantum measurement, and I’d love input on whether this overlaps existing theories (like GRW, CSL, or Penrose), or whether it's worth developing into a formal proposal.

My core idea is: Measurement in QM can be modeled as “cause” — and collapse is triggered when the system becomes causally committed to an outcome.

In standard quantum mechanics, measurement is treated as an axiom (projection postulate), not as an emergent process. I propose modeling the collapse of the wavefunction as a function of “cause”, where cause can emerge from entropy reduction, agency, complexity, or interaction.

• Model structure: Let the state evolve as:

|\psi(t)\rangle = \sum_i c_i(t)|i\rangle

Define a cause function as:

\mathcal{C}(t) = 1 - \sum_i |c_i(t)|^4

(This is a purity-based measure: 0 when fully collapsed, maximal when amplitudes are equal.)

Then modify the Schrödinger equation:

i\hbar \frac{d}{dt}|\psi(t)\rangle = \hat{H}|\psi(t)\rangle + \lambda \cdot \mathcal{C}(t) \cdot \hat{P}_{\text{collapse}}[\psi(t)]

Where:

is a strength parameter (like collapse rate),

is a nonlinear projection-like operator.

•Collapse behavior:

When : superposition strong → collapse-driving term activates

As state collapses: → system stabilizes in eigenstate

This causes a smooth collapse, not an abrupt projection

•Why this is interesting:

Collapse becomes an emergent, mathematically modeled process. Could be tuned with system complexity, entropy, or observer involvement. May bridge classical cause-effect logic with quantum theory. Predicts collapse timescales without relying on environmental decoherence

Conceptually overlaps decoherence and objective collapse models, but reframed as a causality function

Has this causal-collapse direction been studied under different names? Are there known objections to using state purity or entropy as a collapse trigger? I’d appreciate links to any relevant papers or constructive feedback on whether this could fit into the broader quantum foundations conversation.